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Infinitely Continued III (Posted on 2010-02-04) Difficulty: 3 of 5

√(6+2√(7+3√(8+4√(9+5√(10+ ....)))))

See The Solution Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

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re: Is my reasoning valid? | Comment 3 of 7 |
(In reply to Is my reasoning valid? by Jer)


I don't think your "proof' is quite valid either, but I certainly think you are on to something.

The expression is not infinite for x <=2, and by substitution we can see easily enough that f(2) = 2

But I don't see offhand how to use induction to get f(3) = 3,
because (f(x)^2 - x - 2)/(x-2) is undefined when x = 2

If we could prove that f(3) = 3, then it follows that f(x) = x.

  Posted by Steve Herman on 2010-02-04 18:00:52
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